A Robust Experimental Design for Conceptual Model Discrimination Based on Information Theory

This study introduces firm information gain for model discrimination based on Shannon entropy and worst-case scenario experimental design. Firm information gain is the minimal additional information gained by an experimental design with respect to existing information. Robust experimental design aims to maximize the firm information gain by searching for the least number of new pumping wells and observation wells. Robust experimental design includes a Bayes factor threshold to ensure that new data provide strong evidence for model discrimination. To maximize the firm information gain, a framework is proposed that combines the parallel-sequential genetic algorithm (GA) for parallel computing and the nested quadrature rule for efficiently solving multidimensional integrals. The numerical experiment involves the true model for the purpose of verification. The results show that using a full covariance matrix is imperative to avoid exaggerating firm information gain. Collecting new groundwater data is prioritized over exploring additional pumping wells. Maximizing firm information gain is able to identify the same and true model.